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Logic for Linear Algebraists:
150 minutes of logic for proof writing
Courtney R. Gibbons
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\(\newcommand{\NN}{\mathbb N} \newcommand{\ZZ}{\mathbb Z} \newcommand{\QQ}{\mathbb Q} \newcommand{\RR}{\mathbb R} \newcommand{\lt}{<} \newcommand{\gt}{>} \newcommand{\amp}{&} \definecolor{fillinmathshade}{gray}{0.9} \newcommand{\fillinmath}[1]{\mathchoice{\colorbox{fillinmathshade}{$\displaystyle \phantom{\,#1\,}$}}{\colorbox{fillinmathshade}{$\textstyle \phantom{\,#1\,}$}}{\colorbox{fillinmathshade}{$\scriptstyle \phantom{\,#1\,}$}}{\colorbox{fillinmathshade}{$\scriptscriptstyle\phantom{\,#1\,}$}}} \)
Front Matter
Acknowledgements
Colophon
Introduction
1
Connectives
1.1
First Connectives: Not, And, and Or
1.2
Compound Statements
1.3
Conditional and Biconditional Statements
1.4
Exercises
2
Quantifiers
2.1
Propositional Functions
2.2
Exercises
3
Proof Techniques
3.1
Direct Proofs
3.2
Indirect Proofs
3.2.1
Proof by Contrapositive
3.2.2
Proof by Contradiction
3.2.3
Other Logical Equivalences
3.3
Counterexamples
3.4
Exercises
4
Challenging Exercises
Backmatter
A
Style Conventions for Formal Mathematical Writing
A.1
Logic
A.2
Mathematics
A.3
Style
A.4
Examples (and how to write them)
B
Sets
B.1
Functions
B.1
Exercises
B.2
Equivalence relations on sets
Colophon
Acknowledgements
Acknowledgements
Many thanks to Professors Debra Boutin and Sally Cockburn for contributing problems to these notes (and for being wonderful mentors to their colleagues at Hamilton College).
